Bivariate Distributions With Exponential Conditionals
研究了最一般的双变量分布类，其中两组条件密度均为指数形式，发现联合密度必须正比于exp(-λx-μy-νxy)，并推导了分布性质、参数估计和模拟方法，对统计建模和数据分析有参考价值。
Abstract It is frequently easier to visualize conditional distributions of experimental variables rather than joint distributions. In this article we consider the most general class of bivariate distributions such that both sets of conditional densities are exponential. The class proves to be remarkably simple to describe: The joint density must be proportional to exp(- λx - μy - νxy), where the constant of proportionality depends on the classical exponential integral. The joint distribution has marginals that are not exponential and a negative correlation coefficient, except in the special case of independence. After deriving some distributional results, we develop methods for parameter estimation and simulation. A simple method-of-moments estimator appears to give reasonable results. We also briefly discuss generalizations to higher dimensions and to distributions with conditionals in a general exponential family.